Türkü Özlüm ÇELİK Group

In this paper, we construct solutions of the open WDVV equations starting from any Hurwitz Dubrovin–Frobenius manifold. The WDVV equations play a crucial role in the structure of Frobenius manifolds, quantum cohomology, and integrable systems. Extending these ideas, the open WDVV equations provide a framework to incorporate boundary conditions, making them fundamental in open Gromov–Witten theory. Using Dubrovin's construction of Landau–Ginzburg superpotentials associated with Hurwitz spaces, we demonstrate that their primitives satisfy the open WDVV equations. Our approach provides an efficient method for computing open WDVV solutions associated with any Hurwitz Dubrovin–Frobenius manifold.

This paper explores hyperboloid models as statistical manifolds through the framework of flat F-manifolds. We show that these models admit a flat F-manifold structure, offering an alternative to the Fisher information metric.